なら derives from a shortening of ならば, which consists of the 未然形 of 為(な)る and the particle は. In Classical Japanese, both the 未然形 (here なら) and the 已然形 (here なれ) could be used together with ば to express a condition, the former referring to an unrealized condition ("if it happens") and the latter referring to a realized condition ("as it has happened").

Note that 成る - to become is a more recent usage, 為り is simply a copula like である. So なら(ば) corresponds to であらば.

This answers your question, なら corresponds to the "as ... won't"-part of the translation.

なら derives from a shortening of ならば, which consists of the 未然形 of 為(な)る and the particle は. In Classical Japanese, both the 未然形 (here なら) and the 已然形 (here なれ) could be used together with ば to express a condition, the former referring to an unrealized condition ("if it happens") and the latter referring to a realized condition ("as it has happened").

Note that 成る - to become is a more recent usage, 為り is simply a copula like である. So なら(ば) corresponds to であらば.

This answers your question, なら corresponds to the "as ... won't"-part of the translation.

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為る might be relative with なり, but they are usually consider different.
なり came from にあり.
為 is a Chinese copula. Sometime 為る is used as a copula, but it is usually read as たる, which came from とあり. 為人臣者=>人に臣たるもの.

This なら is a conjunction. どうせ間に合わない is your condition, and ゆっくり行こう is the conclusion. なら can bind/connect them together.

See,
雨 (your condition)
行かない(your conclusion) These two can be connected by なら: 雨なら行かない。(*This case must be 助動 in the link, perhaps, because it's 'rain', not a sentence, as animelover and YangMuye said.)
お金がない(condition)
出さなくてよい(conclusion):お金がないなら出さなくてよい。